RE: st: biprobit

Just a follow-up question to Marc's clear discussion of bivariate probit... Suppose that one finds rho is not significantly different from zero in the case of a simultaneous probit model. Does that mean that you can treat the endogenous dichotomous regressor as exogenous when you estimate the two probits separately? In other words, is rho a de facto exogeneity test as well? My understanding is that you can include the observed dichotomous regressor on the rhs, even though its endogenous, BECAUSE you are estimating with a bivariate probit (Greene 2003, p. 716).
Karen Conway
-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Marc F. Bellemare
Sent: Wednesday, October 13, 2004 7:22 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: biprobit
Hi Victoria:
A bivariate probit will estimate a pair of probits. For example, you might
want to estimate simultaneously whether or not a college student works
during a given semester (y_{1} = 1 if she works, 0 otherwise) and whether
or not she drops out of school (y_{2} = 1 if she drops out of school, 0
otherwise). If you need to see the likelihood function of the bivariate
probit, turn to Maddala (1983) (maybe Gouriéroux, 2001, also has it).
It can be used whenever you have a simultaneous or sequential pair of
probits. The coefficients are indeed consistent, assuming the hypotheses of
maximum likelihood estimation are satisfied and the regularity conditions
hold true.
The main question is: should you estimate a bivariate probit or two
separate probits? The biprobit command will return a correlation
coefficient ("rho") which is the correlation coefficient between the
residuals of each of the two probits. If rho is statistically significantly
different from zero, then you should estimate the two probits
simultaneously. If rho is not statistically significantly different from
zero, then you can stick to estimating two separate probits.
Marc
At 09:13 AM 10/13/2004 -0300, you wrote:
>Hi,
>
>I need your help.
>
>Does anybody knows exactly, theoretically speaking, what the biprobit
>comando does? When exactly can be used? Are the coefficients
>consistent?
>
>Thank you all for your help.
>
>Victoria ROdriguez
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__________
Marc F. Bellemare
Ph.D. Candidate
Department of Applied Economics and Management
Cornell University
Ithaca, NY 14853-7801
http://www.people.cornell.edu/pages/mfb24
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